# Adding and subtracting rational expressions. Please help?

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• Nov 14th 2012, 02:19 PM
adamk
Adding and subtracting rational expressions. Please help?
I have a math problem and the answer to it. The only problem I have is that I cannot figure out how to get the answer given. I have posted a picture of the math problem below please help me understand this math problem. I would greatly appreciate it.
• Nov 14th 2012, 02:28 PM
MacstersUndead
Re: Adding and subtracting rational expressions. Please help?
Note that 5p^2 + 16p - 16 = (p+4)(5p-4), which helps somewhat. Make it a habit to try and factorize quadratics when given this kind of problem to aid in finding easy common denominators.

In this problem, we could make the common denominator of each term (4-5p)(5p-4)(p+4).

For example, this would mean that in the first term the numerator would be 8(5p-4)(p+4).
Do the same for the other two terms.
Combine the terms.
Simplify the numerator.
Divide by monomials ex. (4-5p),(5p-4),(p+4) if possible.

done. :)
• Nov 14th 2012, 02:34 PM
adamk
Re: Adding and subtracting rational expressions. Please help?
Im still confused could you elaborate a little more?
• Nov 14th 2012, 02:37 PM
MacstersUndead
Re: Adding and subtracting rational expressions. Please help?
What would you like elaborated?
• Nov 14th 2012, 03:03 PM
adamk
Re: Adding and subtracting rational expressions. Please help?
Attachment 25722 here is where im stuck I got to this point I dont know what to do now?
• Nov 14th 2012, 03:12 PM
MacstersUndead
Re: Adding and subtracting rational expressions. Please help?
Assuming that your expansions are correct, all that's left to do on the numerator is to collect like terms. In this example, we can reorder the numerator as

40p^2 - 10p^2 -5p^2 + 160p - 32p -8p -40p + 4p + 20p - 128 + 32 - 16 which can be rewritten as
(40 - 10 - 5)p^2 + (160 - 32 - 8 - 40 + 4 + 20)p + (-128 + 32 - 16)

Simplify, and then you're done. :)
• Nov 14th 2012, 04:30 PM
adamk
Re: Adding and subtracting rational expressions. Please help?
alright so i have combined everything and I am stuck again. 25p^2+104p-112/(4-5p)(5p-4)(p+4) I dont know what to do from here to get the answer am I even close it says the answer is -9p-44/(5p-4)(p+4)
• Nov 14th 2012, 04:44 PM
MacstersUndead
Re: Adding and subtracting rational expressions. Please help?
(-9p-44) * (4-5p) = 45p^2 - 36p +140p - 176 = 45p^2 -104p - 176 , so somewhere along the way you did not expand correctly. You are close, however. Try again from scratch and use the same general process I introduced. If you cannot solve it after a meaningful effort, I'll write a full detailed solution.
• Nov 14th 2012, 05:41 PM
adamk
Re: Adding and subtracting rational expressions. Please help?
alright so i have combined everything and I am stuck again. 25p^2+104p-112/(4-5p)(5p-4)(p+4) I dont know what to do from here to get the answer am I even close it says the answer is -9p-44/(5p-4)(p+4)
• Nov 14th 2012, 06:11 PM
adamk
Re: Adding and subtracting rational expressions. Please help?
Idk what to do. Ive been working on this same problem all day for like probably 5 hours now. Could u help me out and give me a detailed solution
• Nov 14th 2012, 06:14 PM
MacstersUndead
Re: Adding and subtracting rational expressions. Please help?
Alright, here's a detailed answer. You must have done something wrong in the middle steps, but the concept of common denominator is still the same. Let us consider each term seperately and simplify

$\frac{8}{4-5p} = \frac{8(5p-4)(p+4)}{(4-5p)(5p-4)(p+4)} = \frac{40p^2 -32p + 160p - 128}{(4-5p)(5p-4)(p+4)}$
$\frac{-2}{5p-4} = \frac{-2(4-5p)(p+4)}{(4-5p)(5p-4)(p+4)} = \frac{10p^2 + 32p - 32}{(4-5p)(5p-4)(p+4)}$
$\frac{(p-4)}{(5p-4)(p+4)} = \frac{(p-4)(4-5p)}{(4-5p)(5p-4)(p+4)} = \frac{24p - 5p^2 - 16}{(4-5p)(5p-4)(p+4)}$

Combining the fractions and like terms like we did before we get
$\frac{45p^2 + 184p - 176}{(4-5p)(5p-4)(p+4)}$

While not immediately obvious
$\frac{45p^2 + 184p - 176}{(4-5p)(5p-4)(p+4)} = \frac{-9p-44}{(5p-4)(p+4)}$

since (4-5p) divides (45p^2 + 184p - 176). You can use polynomial long division to verify.

If you have any more questions, let me know. I still want you to practice your skills and challenge your knowledge base so you are ready for exams EDIT:// computation error.
• Nov 14th 2012, 07:34 PM
Wilmer
Re: Adding and subtracting rational expressions. Please help?
Code:

    p - 4            8          2 =============== - ======== - ======== (p + 4)(5p - 4)    5p - 4    5p - 4  p - 4      8    2 ======== - === - === k(p + 4)    k    k
Since 8/(4 - 5p) = -8/(5p - 4), rearrange terms as I show above;
then, to keep "as simple as possible", let k = 5p - 4 (as above).

Now do the "work", then replace k by 5p - 4 : get my drift?